Understand Greatest Common Factor and use it to factor and solve polynomial equations.
Enduring Understanding:
Simplifying equations helps to make the solution clearer and makes it easier to solve for the variable.
Essential Question:
Why might it be helpful in solving an equation to factor out the terms that its elements have in common?
NCTM Standards:
I am honestly having trouble using the NCTM standards. I feel I am more familier with the PA State Standards. The state standard I would use is:
2.1.A1.B Use factoring to create equivalent forms of polynomials
Performance Activity:
Cooperative Group Activity
Least Common Multiple and Greatest Common Factor Objectives:
The learner will
practice the computation of the least common multiple and the greatest common factor.
derive the relationship among the least common multiple, the greatest common factor, and the product of the two numbers.
record data systematically and discern a pattern for analyzing data.
Group Size: Four Materials for Each Group:
4 problem sheets, 1 record sheet, 1 envelope with 12 slips of paper with a pair of numbers Activity Instructions:
Appoint a reader and a recorder for each group. One person should read the instructions while other group members follow along. When the reader has completed the reading, others may question or explain the tasks and the requirements of the problem. When the group is ready to begin, each member should select, at random, three slips of paper from the number envelope.
Each person receives three pairs of numbers. Analyze each pair of numbers
(m, n), to determine— a) the greatest common factor of m and n: GCF (m, n) b) the least common multiple of m and n: LCM (m, n) c) the product of m and n: m.n Example: GCF (4, 6) = 2, LCM (4, 6) = 12, m.n = 24.
Each group member who has completed his or her part of the work should offer to help another member.
Group members who have completed their work should exchange papers and check one another’s results.
When all pairs of numbers have been analyzed, the recorder should list all group results on the record sheet.
When the group has agreed on the results, the members should discuss their findings and determine the relationships among the greatest common factor, the least common multiple, and the product of any two numbers.
State the relationship. Then test it on four new pairs of numbers, one pair chosen by each group member.
The recorder should record the group’s work on the record sheet.
Record Sheet for LCM and GCF Cooperative Group Activity
Factoring
Objective:
Understand Greatest Common Factor and use it to factor and solve polynomial equations.Enduring Understanding:
Simplifying equations helps to make the solution clearer and makes it easier to solve for the variable.Essential Question:
Why might it be helpful in solving an equation to factor out the terms that its elements have in common?NCTM Standards:
I am honestly having trouble using the NCTM standards. I feel I am more familier with the PA State Standards. The state standard I would use is:2.1.A1.B Use factoring to create equivalent forms of polynomials
Performance Activity:
Cooperative Group Activity
Least Common Multiple and Greatest Common Factor
Objectives:
The learner will
- practice the computation of the least common multiple and the greatest common factor.
- derive the relationship among the least common multiple, the greatest common factor, and the product of the two numbers.
- record data systematically and discern a pattern for analyzing data.
Group Size: FourMaterials for Each Group:
4 problem sheets, 1 record sheet, 1 envelope with 12 slips of paper with a pair of numbers
Activity Instructions:
- Appoint a reader and a recorder for each group. One person should read the instructions while other group members follow along. When the reader has completed the reading, others may question or explain the tasks and the requirements of the problem. When the group is ready to begin, each member should select, at random, three slips of paper from the number envelope.
- Each person receives three pairs of numbers. Analyze each pair of numbers
(m, n), to determine—a) the greatest common factor of m and n: GCF (m, n)
b) the least common multiple of m and n: LCM (m, n)
c) the product of m and n: m . n
Example: GCF (4, 6) = 2, LCM (4, 6) = 12, m . n = 24.
- Each group member who has completed his or her part of the work should offer to help another member.
- Group members who have completed their work should exchange papers and check one another’s results.
- When all pairs of numbers have been analyzed, the recorder should list all group results on the record sheet.
- When the group has agreed on the results, the members should discuss their findings and determine the relationships among the greatest common factor, the least common multiple, and the product of any two numbers.
- State the relationship. Then test it on four new pairs of numbers, one pair chosen by each group member.
- The recorder should record the group’s work on the record sheet.
Record Sheet for LCM and GCF Cooperative Group ActivityNumber Pairs (m, n)
GCF (m, n)
LCM (m, n)
Product (m . n)